Proof nets Construction and Automated Deduction in Non-Commutative Linear Logic

Proof nets can be seen as a multiple conclusion natural deduction system for Linear Logic (LL) and form a good formalism to analyze some computation mechanisms, for instance in type-theoretic interpretations. This paper presents an algorithm for automated proof nets construction in the non-commutative multiplicative linear logic that is useful for applications including planning, concurrency or sequentiality. The properties of this algorithm can be proved from a recently defined graph-theoretic characterization of non-commutative proof nets. Involving simple construction principles improved in the commutative case, it leads also to a new proof search method for the non-commutative fragment. Moreover because of the relationships between the non-commutative linear logic and the Lambek calculus we can derive from it an alternate method for automatic construction of proof nets in this calculus.